In the oil industry, electromagnetic (EM) induction surveys are used to map the electrical conductivity of geologic formations between boreholes and/or radially away from a single wellbore. The latter, usually referred to as induction logging, has been in routine use for over fifty years. Those surveys are performed in open holes; that is, holes that have not been lined with a (typically, metal) casing.
Recently, the concepts of induction logging have been extended to surveys between uncased wells and between wells cased with conductive liners. There is also interest in the use of logging between surface and downhole sensors, and within single wells that are cased with conductive liners. The conductive liners (casing) introduce several problems. For example, the signal from the transmitter to the receiver is severely attenuated upon passing through the conductive casing because of the casing's high conductivity and, usually, high magnetic permeability (high-mu or high-μ). The conductivity, permeability, and thickness of the casing wall can vary along the length of the casing. Transmitters in these surveys are normally multi-turn solenoids that have a core of high magnetic permeability. At high current levels in the solenoid, the permeability of the core material, and of the surrounding casing itself, is driven into a nonlinear regime. Under those circumstances, the current in the solenoid is not proportional to the net radiated field. Receivers may also use high-mu, cored solenoids, but because they never operate at the high field levels in which such nonlinear effects are seen, this is not a problem for them, in practice. However, receiver coils have many more turns than transmitter coils, and the large winding stray capacitance combined with large coil inductance can produce a resonant peak within the frequency range of operation. This should be accounted for when relating the measured impedance to that of an ideal inductor or the actual casing attenuation factors to those of an ideal inductor.
The various types of induction surveys typically share many commonalities. A transmitter, usually a multi-turn coil of wire, carries an alternating current of frequency ω (radians/sec). This creates a time-varying magnetic field in the surrounding formation that in turn, by Faraday's law, induces an electromotive force (emf). This emf drives currents in the formation that are basically proportional to the formation conductivity. Finally, a receiver is positioned either in the same hole as the transmitter, in another hole, or on the surface (land or seafloor), and measures the magnetic field arising from the transmitter and the secondary or induced currents in the formation. Conventional induction logging always uses a combination of multiple receivers and/or multiple transmitters connected in series so as to cancel the mutual signal in air. In general, a theoretical model for a logging system embedded in a formation of arbitrary resistivity is used to match or interpret the received signals. In some applications, the absolute value of the average formation resistivity is not as important as the ability to map variations of resistivity within the formation. To determine this spatial variation of formation resistivity, the surveys typically involve placing the transmitter at multiple locations in the hole and measuring the fields at multiple receiver locations for each transmitter location. In crosshole surveys, this yields a data set similar to those obtained from tomography.
There is a “window” of frequencies in which such surveys are practical. Below a certain frequency, the secondary fields from the formation are simply too small relative to the primary coupling between the transmitter and receiver to be measured accurately with practical receivers. Above a certain frequency, the casing attenuation obliterates the formation response. The frequency window depends greatly on the type of casing used. Carbon steel casing generally has a conductivity (σ) of approximately five million S/m and a relative permeability (μr) of approximately 100. Chromium casing is essentially non-magnetic (μr is equal to or close to 1), and has a conductivity of approximately one million S/m. As a result, chromium casing is preferable because it attenuates the EM signal much less than the carbon steel casing, at the same frequency. Thus, for practical field systems in chromium cased boreholes, this window can be up to several hundred Hz, while in carbon steel cased boreholes, the frequency is limited to roughly one hundred Hz and below.
Recall, however, that even in those frequency windows, the casing properties (i.e., conductivity (σ), relative permeability (μr), thickness (t), and inner/outer diameter) are not constant along the length of casing. Since the casing attenuation is so strong, small variations in the casing's properties produce variations in the fields seen by a receiver that are large compared to the variations expected from desired formation variations. A further problem is that the strength of the transmitter, known as its effective moment, must be known so that moment variations are not misinterpreted as variations in the formation conductivity.
The inhomogenieties of well casing alluded to above make it challenging to remove the casing imprints on EM data to get high resolution inversion images. Some previously attempted methods related to casing imprints removal are software-based methods, while others are measurement-based. Some measurement-based prior art methods involve using numerical modeling codes to calculate casing attenuation factors and coil impedance as functions of parameter(s) related to casing properties and frequency, and then using measured coil impedance at given frequencies to interpolate for corresponding casing attenuation factors. Alternatively, one can build up a look-up table and then search for the corresponding conductive casing attenuation factor for the measured impedance at given frequencies.
The above casing correction methods are based on the assumption that the casing effects and formation effects are separable, which was concluded from studies assuming the use of point-dipole transmitters and receivers in steel casing. However, due to the fairly large size of cross-well transmitter and receiver coils, experiments in steel casing at a surface test facility have shown that the point-dipole model fails at distances less than about 300 ft away from the casing when casing collar or casing centralizers are present in the vicinity of the induction coil disposed inside the casing. A proposed solution to this problem for a transmitter in chromium casing is to use only the receiver data (as a function of transmitter depth) when the transmitter is in relatively uniform sections of the casing, thereby eliminating the effect of casing collars and centralizers. An alternative proposed solution to this same problem for receivers in conductive casing is to identify casing collars and casing centralizers using a receiver casing coupling identification (CCID) log (a receiver depth log of trans-impedance between the receiver feedback winding and the main winding) to avoid placing receiver stations near casing collars and casing centralizers during a survey.
The induction coil used for crosswell, surface-to-borehole, and single-well applications has at least two modes of operation: (1) straight (ST) mode; and (2) feedback (FB) mode. Straight mode operation measures the voltage of the main winding wound on a high magnetic permeability core. It has a resonance peak due to winding stray capacitance within a desired frequency range. Feedback mode is when the main winding voltage is connected to the feedback winding through a feedback circuit, which results in a flat frequency response within a desired frequency range. For ST mode, an equivalent circuit model relates measured coil impedance in casing to modeled impedance of an ideal inductor using numerical modeling. For induction coils in FB mode, there are several ways to implementing feedback circuit. For example, one type of feedback circuit was used on low-frequency induction magnetometers having relatively small dimensions for space research. FB mode in air is not particularly sensitive to environmental parameters such as temperature and pressure, and it has larger signal to noise in steel casing compared to ST mode. On the other hand, certain impedance methods relate the impedance of the main winding to ST mode casing attenuation factors. Experimental and modeling studies have shown that a receiver in FB mode is less attenuated by conductive casing compared to a receiver in ST mode, and the FB casing attenuation factors can be obtained from ST mode casing factors.